1132 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1952 



The fields of the principal mode in both plane and coaxial Clogston 2 

 lines will be plotted in the next section, when we shall also be able to 

 show the fields in various transition structures between the extreme 

 Clogston 1 and the complete Clogston 2. 



As a numerical example, let us compare the attenuation constant of a 

 conventional coaxial cable with that of a completely filled Clogston 2 

 cable of the same size. If a and h denote the radii of the inner and outer 

 conductors of a conventional coaxial cable of optimum proportions 

 (5/a = 3.5911), then at frequencies high enough to give a well-developed 

 skin effect on both conductors, the attenuation constant is given by 

 equation (151) of Section IV, namely 



1.796 , . 



oc = —r , (317) 



where rjo is the intrinsic impedance of the main dielectric, which may be 

 air. On the other hand, the attenuation constant of a Clogston 2 cable 

 of outer radius h, with infinitesimally thin laminae and no inner core, 

 is, from equations (282), (291), and (310), 



7.341 ^ ^ 



« = /^-,, . (318) 



It will be shown in the next section that for infinitesimally thin laminae 

 whose permeabilities are all equal, the optimum value of 6 is 2/3. As- 

 suming no magnetic materials and setting 6 = 2/3, we find that the 

 ratio of the attenuation constant ac of the Clogston cable to the at- 

 tenuation constant «« of an air-filled standard coaxial cable of the same 

 size, made of the same conducting material, is 



a./«3 = 10.62 V^ 8i/b. (319) 



For copper conductors, 5i is given by equation (78) of Section III, 

 and the crossover frequency above which the Clogston cable has a 

 lower attenuation constant than the standard coaxial cable turns out 

 to be 



/mo = 763.5€2r/&mil8 , (320) 



where frequency is measured in Mc-sec~ and the radius of the cable 

 in mils. We also note that at the crossover frequency the electrical radius 

 of the inner conductor of the standard coaxial is 2.96 v'€2r ^i » so that 

 the use of equation (317) for a, appears to be (barely) justified. Applying 

 equation (320) to an ideal Clogston 2 cable of outer diameter 0.375 

 inches, excluding the sheath, with copper conductors, polyethylene 



